New Einstein-Sasaki Spaces in Five and Higher Dimensions

2005/04/30 by Mirjam Cvetič, M. Cvetic, H. Lü +4 · 9 citations
Mathematics · Physics and Astronomy · #Anti-de Sitter space #Black Holes and Theoretical Physics #Boundary (topology) #Dual polyhedron #Einstein #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Invertible matrix #Isometry (Riemannian geometry) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Quiver #gr-qc #hep-th #math.DG

paper · pdf · doi:10.1103/physrevlett.95.071101

published as Phys.Rev.Lett.95:071101,2005 · Revtex, 4 pages, metric regularity conditions are further refined

arxiv created 2005/05/27 · openalex publication_date 2005/08/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We obtain infinite classes of new Einstein-Sasaki metrics on complete and nonsingular manifolds. They arise, after Euclideanization, from BPS limits of the rotating Kerr--de Sitter black hole metrics. The new Einstein-Sasaki spaces L^p,q,r in five dimensions have cohomogeneity 2 and U(1)\ifmmode×\else\texttimes\fiU(1)\ifmmode×\else\texttimes\fiU(1) isometry group. They are topologically S²\ifmmode×\else\texttimes\fiS³. Their AdS/CFT duals describe quiver theories on the four-dimensional boundary of AdS₅. We also obtain new Einstein-Sasaki spaces of cohomogeneity n in all odd dimensions D=2n+1\ensuremath≥5, with U(1)ⁿ⁺¹ isometry.

Citations

• Rotating Black Holes in Gauged Supergravities; Thermodynamics, Supersymmetric Limits, Topological Solitons and Time Machines
• Supersymmetric Kerr–anti-de Sitter solutions
• The general Kerr–de Sitter metrics in all dimensions
• Rotating Black Holes in Higher Dimensions with a Cosmological Constant
• The large N limit of superconformal field theories and supergravity

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• Free Yang-Mills theory versus toric Sasaki-Einstein manifolds
• Higher-dimensional black holes: hidden symmetries and separation of variables
• On the supersymmetric limit of Kerr-NUT-AdS metrics